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1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...

The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

Two planes that do not intersect are said to be parallel. Two planes specified in Hessian normal form are parallel iff |n_1^^·n_2^^|=1 or n_1^^xn_2^^=0 (Gellert et al. 1989, ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The center J_i of an excircle. There are three excenters for a given triangle, denoted J_1, J_2, J_3. The incenter I and excenters J_i of a triangle are an orthocentric ...

The approximation for pi given by pi approx sqrt((40)/3-2sqrt(3)) (1) = 1/3sqrt(120-18sqrt(3)) (2) = 3.141533.... (3) In the above figure, let OA=OF=1, and construct the ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

A line and a plane are parallel if they do not intersect.